Express this quotient in scientific notation: ${\frac{7.760\times 10^{1}} {8.0\times 10^{-2}}}$
Solution: Start by collecting like terms together. $= {\frac{7.760} {8.0}} \times{\frac{10^{1}} {10^{-2}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.97 \times 10^{1\,-\,-2}$ $= 0.97 \times 10^{3}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.97$ is the same as $9.70 \div 10$ , or $9.70 \times 10^{-1}$ $ = {9.70 \times 10^{-1}} \times 10^{3} $ $= 9.70\times 10^{2}$